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 March 16th, 2012, 08:46 PM #1 Member   Joined: Sep 2010 Posts: 63 Thanks: 0 Price Elasticity, Separation of Variables So I naively took price elasticity http://en.wikipedia.org/wiki/Price_elasticity_of_demand http://en.wikipedia.org/wiki/Elasticity_%28economics%29 Ed = ((Qd-Qo)/Qd)/((Pd-Po)/Pd)) In the differential form: Ed = (P/Q)*dQ/dP Separated variables: (Ed/P)dP = (1/Q)dQ Integrated the left from Po to P and the right from Qo to Q and got the incredibly borrowing result: exp(Ed)(P/Po)=Q/Qo Which essentially says that the only functions that can satisfy constant price elasticity are a non negative slopping line though the origin. Now, this result is disappointing because this does not look like a typical demand curve at all, yet price elasticity is used to consider effects on total revenue due to changes in quantities: http://en.wikipedia.org/wiki/Total_revenue_test I was expecting a function that would be able to interpolate a demand function well so I could approximate a small a small region of the curve with constant elasticity. I could use the non differential form but I was expecting them to agree over a small region and am wondering what I might have done wrong. Reviewing separation of variables: http://en.wikipedia.org/wiki/Separation_of_variables I see I forgot an absolute value sign. This will also gives me negative slope solutions but I'm still restricted to lines that go though the origin. : Pauses and scratches head : Tags elasticity, price, separation, variables Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Dratilhelvete Economics 0 March 12th, 2014 11:43 AM PKA111 Calculus 2 January 27th, 2013 11:14 AM edwinh Calculus 7 August 11th, 2012 01:53 PM tsl182forever8 Calculus 5 March 3rd, 2012 01:11 PM engininja Calculus 2 February 22nd, 2011 01:06 PM

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